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POST UTME AAUA 2025 Physics | Objective

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Question 1

A 5.0 kg block is attached to a horizontal, massless spring with a force cons\tant of 200 N/m. The block is displaced by 0.25 m from its equilibrium position and released from rest. Assuming the block undergoes simple harmonic motion, determine the maximum speed of the block.

A. 2.5 m/s

Correct B. 5.0 m/s

C. 10.0 m/s

D. 20.0 m/s

Correct Answer: B

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Question 2

A wave with a frequency of 50 Hz and a wavelength of 0.5 m is traveling through a medium. If the wave has a speed of 20 m/s, determine the amplitude of the wave.

A. 0.01 m

B. 0.1 m

Correct C. 0.5 m

D. 1.0 m

Correct Answer: C

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Question 3

A capacitor consists of two parallel plates, each with an area of 0.1 m^2 and separated by a dis\tance of 0.01 m. If the capaci\tance is 10^-6 F, determine the charge stored on one plate when a potential difference of 10 V is applied across the capacitor.

A. 10^-8 C

B. 10^-7 C

Correct C. 10^-6 C

D. 10^-5 C

Correct Answer: C

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Question 4

A block of mass 2.0 kg is placed on a horizontal, frictionless surface. A horizontal force of 10 N is applied to the block, cau\sing it to accelerate at 2.0 m/s^2. Determine the force exerted by the surface on the block.

A. 10 N

B. 20 N

C. 30 N

Correct D. 40 N

Correct Answer: D

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Question 5

A projectile is launched from the ground with an initial velocity of 20 m/s at an angle of 60 degrees above the horizontal. Assuming the only force acting on the projectile is gravity, determine the time it takes for the projectile to reach its maximum height.

A. 1.0 s

Correct B. 2.0 s

C. 3.0 s

D. 4.0 s

Correct Answer: B

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Question 6

A block of mass 2 kg is attached to a horizontal, massless spring with a force cons\tant of 100 N/m. The block is displaced by 0.2 m from its equilibrium position and released from rest. Assuming the motion is simple harmonic, calculate the maximum speed of the block.

A. 2 m/s

B. 4 m/s

Correct C. 6 m/s

D. 8 m/s

Correct Answer: C

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Question 7

A parallel plate capacitor has a capaci\tance of 10 μF. If a potential difference of 20 V is applied across the plates, calculate the energy stored in the capacitor.

A. 0.1 J

Correct B. 0.2 J

C. 0.4 J

D. 0.8 J

Correct Answer: B

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Question 8

A particle of mass 1 kg is moving in a circular path with a radius of 2 m. If the particle has a speed of 4 m/s, calculate the centripetal acceleration.

A. 2 m/s^2

Correct B. 4 m/s^2

C. 6 m/s^2

D. 8 m/s^2

Correct Answer: B

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Question 9

A current of 2 A flows through a resistor of 10 Ω. Calculate the power dissipated in the resistor.

Correct A. 20 W

B. 40 W

C. 60 W

D. 80 W

Correct Answer: A

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Question 10

A magnetic field of 0.5 T is applied to a current-carrying wire. If the current is 2 A, calculate the force experienced by the wire.

A. 1 N

Correct B. 2 N

C. 3 N

D. 4 N

Correct Answer: B

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Question 11

A 5% saline solution is prepared by dissolving 5g of NaCl in 95g of water. What is the molar concentration of the solution?

Correct A. 0.05 M

B. 0.1 M

C. 0.2 M

D. 0.25 M

Correct Answer: A

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Question 12

A 100Omega resistor is connected in series with a 200Omega resistor and a 50V battery. What is the current flowing through the 100Omega resistor?

Correct A. 0.25A

B. 0.5A

C. 0.75A

D. 1A

Correct Answer: A

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Question 13

A radioactive sample has a half-life of 10 years. If the initial activity is 100Bq, what is the activity after 20 years?

Correct A. 12.5Bq

B. 25Bq

C. 50Bq

D. 100Bq

Correct Answer: A

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Question 14

A 2kg block is attached to a horizontal spring with a force cons\tant of 100N/m. If the block is displaced by 0.1m from its equilibrium position, what is the potential energy stored in the spring?

A. 1J

B. 2J

C. 5J

Correct D. 10J

Correct Answer: D

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Question 15

A 50Omega resistor is connected in parallel with a 100Omega resistor. What is the equivalent resis\tance?

A. 25Omega

B. 30Omega

C. 50Omega

Correct D. 75Omega

Correct Answer: D

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Question 16

A particle of mass $m$ is confined to a one-dimensional box of length $L$. The ground state wave function of the particle is given by $psi_0(x) = \sqrt{\frac{2}{L}} \sinleft$ \frac{pi x}{L}\right $$. What is the expectation value of the position operator for this state?

A. 0

Correct B. L/2

C. L

D. L/4

Correct Answer: B

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Question 17

A circuit consists of a resistor $R$, an inductor $L$, and a capacitor $C$ connected in series. The circuit is driven by an alternating voltage source with a frequency of $f$. What is the impedance of the circuit at resonance?

A. R

B. L

C. C

Correct D. \sqrt{R^2 + $ X_L - X_C $^2}

Correct Answer: D

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Question 18

A heat engine operates between two temperatures $T_1$ and $T_2$. The engine has an efficiency of $\eta$. What is the ratio of the high-temperature reservoir to the low-temperature reservoir?

A. 1

B. 1/\eta

Correct C. 1/$ 1-\eta $

D. \eta

Correct Answer: C

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Question 19

A vector $\vec{A}$ has a magnitude of $A$ and makes an angle $\theta$ with the positive x-axis. What is the x-component of the vector?

Correct A. A \cos\theta

B. A \sin\theta

C. A \tan\theta

D. A \csc\theta

Correct Answer: A

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Question 20

A body of mass $m$ is moving in a circular path of radius $r$ with a cons\tant speed $v$. What is the magnitude of the centripetal acceleration?

Correct A. v^2/r

B. v/r

C. r/v

D. v^2

Correct Answer: A

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Question 21

A gas is heated from 300 K to 400 K at cons\tant volume. If the initial pressure is 1.2 atm, what is the final pressure?

A. 1.5 atm

Correct B. 2.0 atm

C. 2.5 atm

D. 3.0 atm

Correct Answer: B

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Question 22

A magnetic field is produced by a current-carrying wire. If the current is 5 A and the length of the wire is 2 m, what is the magnetic field strength at a dis\tance of 1 m?

A. 0.25 T

Correct B. 0.50 T

C. 0.75 T

D. 1.00 T

Correct Answer: B

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Question 23

A sound wave has a frequency of 200 Hz and a wavelength of 0.5 m. What is the speed of the sound wave?

A. 100 m/s

Correct B. 200 m/s

C. 300 m/s

D. 400 m/s

Correct Answer: B

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Question 24

A heat engine operates between 300 K and 400 K. If the efficiency is 30%, what is the temperature of the hot reservoir?

A. 350 K

B. 400 K

Correct C. 450 K

D. 500 K

Correct Answer: C

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Question 25

A simple harmonic motion has a frequency of 5 Hz and an amplitude of 0.2 m. What is the angular frequency?

A. 10 rad/s

Correct B. 20 rad/s

C. 30 rad/s

D. 40 rad/s

Correct Answer: B

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